Calculus Examples

$- {(c - 8)}^{2}$

Step 1

Rewrite ${(c - 8)}^{2}$ as $(c - 8) (c - 8)$ .

$- ((c - 8) (c - 8))$

Step 2

Expand $(c - 8) (c - 8)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$- (c (c - 8) - 8 (c - 8))$

Step 2.2

Apply the distributive property.

$- (c \cdot c + c \cdot - 8 - 8 (c - 8))$

Step 2.3

Apply the distributive property.

$- (c \cdot c + c \cdot - 8 - 8 c - 8 \cdot - 8)$

$- (c \cdot c + c \cdot - 8 - 8 c - 8 \cdot - 8)$

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $c$ by $c$ .

$- (c^{2} + c \cdot - 8 - 8 c - 8 \cdot - 8)$

Step 3.1.2

Move $- 8$ to the left of $c$ .

$- (c^{2} - 8 \cdot c - 8 c - 8 \cdot - 8)$

Step 3.1.3

Multiply $- 8$ by $- 8$ .

$- (c^{2} - 8 c - 8 c + 64)$

$- (c^{2} - 8 c - 8 c + 64)$

Step 3.2

Subtract $8 c$ from $- 8 c$ .

$- (c^{2} - 16 c + 64)$

$- (c^{2} - 16 c + 64)$

Step 4

Apply the distributive property.

$- c^{2} - (- 16 c) - 1 \cdot 64$

Step 5

Simplify.

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Step 5.1

Multiply $- 16$ by $- 1$ .

$- c^{2} + 16 c - 1 \cdot 64$

Step 5.2

Multiply $- 1$ by $64$ .

$- c^{2} + 16 c - 64$

$- c^{2} + 16 c - 64$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$